Largely you are correct. It works like this.
If you are a net exporter, you are essentially giving away your own output to a foreign nation in exchange for bits of paper. The reason you can't spend that paper is that it would destroy your exports (your own currency would go sky high as the system tried to eliminate the imbalance) and you'd have to find something else for the people working in exports to do, or you'd get a Dutch Disease problem internally (and likely end up in a situation like Venezuela)
So Botswana sells its natural assets to the US in exchange for US dollars. Those US dollars find their way into the bowels of the financial system and are discounted into the local currency. Either directly - like the Chinese do, or indirectly via some fancy financial system (normally a Sovereign Wealth fund, or Pension schemes with compulsory contributions). They then sit there (the Norwegian fund for example cannot spend anything - ever) - largely to avoid a Dutch disease in the country and to stop the local currency appreciating against the export target.
The result is that the rich countries get stuff essentially for free from the poorer countries so that the poorer countries can issue their own money without people getting agitated.
The whole thing is a conjuring trick. The poorer country would be better putting people to work creating domestic infrastructure straight away and only exporting what is necessary to get needed goods and services required to create that infrastructure. But to do that requires you to operate the central bank in a way that appears 'wrong'. You have to issue liabilities against 'Other Assets' rather than 'US Treasuries' and that upsets people who don't understand how banks actually work.
The GBP/USD gets 'locked' in the financial system. Because it is being used to discount to the scrip used locally you can never get rid of it. To do so would reveal the central bank illusion and explain how the trick is done. Then people might start asking question like: why don't we use our own money in our own circulation to ensure everybody has a job and solve unemployment permanently and forever? And that would never do ;-)